System and method for three-dimensional imaging using scattering from annihilation coincidence photons

ABSTRACT

Systems and methods are described herein for performing three-dimensional imaging using backscattered photons generated from a positron-electron annihilation. The systems and methods are implemented using the pair of photons created from a positron-electron annihilation. The trajectory and emission time of one of the photons is detected near the annihilation event. Using this collected data, the trajectory of the second photon can be determined. The second photon is used as a probe photon and is directed towards a target for imaging. The interaction of the second probe photon with the target produces back scattered photons that can be detected and used to create a three-dimensional image of the target. The systems and methods described herein are particularly advantageous because they permit imaging with a system from a single side of the target, as opposed to requiring imaging equipment on both sides of the target.

PRIORITY CLAIM

This application claims priority to pending U.S. Provisional PatentApplication Ser. No. 61/257,874, filed on Nov. 4, 2009, and titled“Three-Dimensional Imaging System and Technique Using Measured SidewaysScattering From Annihilation Coincidence Photons.” The entire content ofthis prior application is hereby incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to the field of imaging usingphotons and more specifically to imaging using coincidence photonsgenerated from electron-positron annihilation.

2. Description of the Related Art

In positron emission tomography (“PET”) imaging, a radioisotope sourceemits positrons that combine with electrons and annihilate, eachannihilation producing a pair of oppositely directed 511 keV photons.The volume being imaged is placed between a pair of position-sensitivegamma photon detector arrays. The coincident detection of a pair ofphotons on the two detector arrays signals that an annihilation eventhas been detected. The position of the annihilation event can be deducedas having occurred at some point along a straight line joining the twopoints of detection. Time-of-flight information can be used to somewhatfurther localize the position of the annihilation to some section alongthis line, limited by the timing resolution of the photon detectionsystems. The typical application is to use these projected points ofannihilation to build up a three-dimensional map of annihilation densityand measure the uptake of short-lived radioisotopes within humanpatients for diagnostic purposes.

PET imaging systems are designed to localize the position of theradioisotope materials. The invention described in the DetailedDescription of the Exemplary Embodiments that follows modifies the PETimaging process so that annihilation coincidence photons can be used forimaging of other targets.

A landmine detection system has been described by J. R. Tickner, M. P.Currie, and G. J. Roach in “Feasibility study for a low-cost 3Dgamma-ray camera,” Applied Radiation and Isotopes 61 (2004)67-71. Thissystem uses a positron annihilation source to create probe photons withknown directions and time. Instead of the use of a return-scatterdirectional detection technique, time-of-flight is used to establishsome three-dimensional information as to the scattering locations.However, the prior art in time-of-flight scattering measurements usingannihilation coincidence photons lacks accurate resolution in the thirddimension through limitations in the state-of-the-art in radiationdetector timing resolution.

So-called “flying-spot” backscatter imagers utilize a rotatingcollimator and a bremsstrahlung x-ray source to generate a rasteredx-ray beam. When this beam is swept over a target, either by moving thesource or the target through the rastering beam, a two-dimensional imageis formed by detection of photons backscattered from the target. Theflying-spot systems utilizing a bremsstrahlung x-ray source do not imagein the third dimension. Also, because the outgoing probe photons fromthe x-ray source are not mono-energetic, it is not possible to useenergy of the return scattered photons to discriminate single- frommultiple-scatter events. Furthermore, bremsstrahlung x-ray sourcesproduce many x-ray photons at lower energy that have significantlyinferior penetration capability than higher-energy mono-energeticphotons, and consequently produce images with less penetration andreduced contrast for a given fixed radiation dose to the target than amono-energetic source will yield. X-ray equipment also tends to becomplex and requires significant maintenance.

SUMMARY OF THE INVENTION Summary of the Problem

There is a need for an apparatus and a method that provides moreaccurate imaging with scattered photons. This need includes the need formore accurate three-dimensional imaging through imaging of the returnscattered photons from a single side of a target. Single-sided imagingtools have a distinct advantage over imaging systems that require accessto both sides of the target.

Summary of the Solution

The invention improves image quality, contrast and penetration for agiven radiation dose to the target. It does this by reducing uncertaintyin the measurement process, extracting more information from eachscattered photon detected from the target. Each scattered photonreceived can be associated, by timing coincidence, with an outgoingprobe photon. Furthermore, the outgoing probe photon's trajectory hasbeen determined, through measurement of the coincident photon in theannihilation pair, so the position at which the scattering took place iswell localized. This reduces the build up of image variance (noise) inconstructing the three-dimensional image.

In a first exemplary embodiment, a method for creating an image of atarget is described. The method includes arranging a radioisotope sourcethat emits positrons that collide with electrons producing a pair ofphotons. The first of the two photons collides with a gamma detectorwhich measures a first trajectory and a first time associated with thefirst photon. An imaging software module uses the measured firsttrajectory and first time associated with the first photon to calculatea second trajectory and a second time associated with the second photon.The second photon collides with the target and produces a scatteredphoton. An imaging detector detects the scattered photon measuring ascattered trajectory and a scattered time associated with the scatteredtrajectory. The imaging software module can calculate a position for thetarget using the first trajectory, the first time, the second trajectoryand the second time.

In a second exemplary embodiment, a system for creating an image of atarget is described. The system comprises a radioisotope source thatgenerates a positron that collides with an electron producing a pair ofphotons. The system further comprises a photon tagger that detects afirst photon from the photon pair and measures a first trajectory and afirst time associated with the first photon. An imaging software moduleuses the first trajectory and the first time to calculate a secondtrajectory and a second time associated with the second photon. Thesecond photon collides with the target and produces a scattered photon.The system also comprises a detector measuring a scattered trajectoryand a scattered time associated with the scattered photon. The imagingsoftware module can use the first trajectory, the first time, the secondtrajectory and the second time in creating an image of the target.

In a third exemplary embodiment, a computer program product for creatingan image of the target comprises a series of instructions to be executedby a computer. The instructions comprise instructions for receiving afirst trajectory and a first time from a gamma detector, the firsttrajectory and the first time associated with a first photon of a photonpair created by positron-electron annihilation. The instructions furthercomprising instructions for calculating a second trajectory and a secondtime associated with a second photon. The instructions also comprisinginstructions for receiving a scattered trajectory and a scattered timefrom an imaging detector, the scattered trajectory and the scatteredtime associated with a scattered photon created by a collision betweenthe second photon and the target. The instructions further comprisinginstructions for using the second trajectory, the second time, thescattered trajectory and the scattered time for creating an image of thetarget.

These and other embodiments are described in the detailed descriptionthat follows and the associated drawings.

BRIEF DESCRIPTION OF THE FIGURES

The preferred embodiments of the present invention are illustrated byway of example and are not limited to the following figures:

FIG. 1 illustrates the components of a backscatter imaging system inaccordance with an exemplary embodiment of the present invention.

FIG. 2 illustrates the components of a backscatter imaging system inaccordance with an exemplary embodiment of the present invention.

FIG. 3 illustrates the use of a photon tagger in accordance with anexemplary embodiment of the present invention.

FIG. 4 illustrates a coded aperture mask and detector array inaccordance with an exemplary embodiment of the present invention.

FIG. 5 illustrates a reconstruction kernel in accordance with anexemplary embodiment of the present invention.

FIG. 6 illustrates a calculated point-spread function for a codedaperture detector in accordance with an exemplary embodiment of theinvention.

FIG. 7 illustrates simulated reconstructions for single-scatter returnsin accordance with an exemplary embodiment of the invention.

FIG. 8 illustrates Compton scattering of a photon from an electron inaccordance with an exemplary embodiment of the invention.

FIG. 9 illustrates the determination of scattering angle using timinginformation in accordance with an exemplary embodiment of the invention.

FIG. 10 illustrates energy bands for identifying single scatter eventsin accordance with an exemplary embodiment of the invention.

FIG. 11 illustrates a method for imaging a target using backscatterphotons in accordance with an exemplary embodiment of the invention.

FIG. 12 illustrates a computing environment for executing an imagingsoftware module in accordance with an exemplary embodiment of theinvention.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

The invention includes a method using electron-positron annihilationcoincidence photons to form a radiographic image of a volume directly inthree dimensions without the need for multiple source and detectorviewpoints to form said image. The reconstructed image containsthree-dimensional information on radiographic density and also allowssome estimates of the atomic number of the materials imaged in thevolume. Such a system can be used to form three-dimensional images of avolume when access to only one side of the volume is available.

The present invention turns the PET imaging process around. The systemuses a compact radioisotope source in a known location, and thedetection of one of the coincident photons in the pair to determine thetrajectory and emission time of the other photon in the pair. Thismechanism is used to generate a source of photons that have been“tagged” in their direction and time.

The invention described also relies on a return-scatter directionaldetector to measure the arrival time and provide some directionalinformation on the return scattered photons detected from the regionbeing imaged. While there are a number of techniques for doing suchdetection, coded-aperture imagers are the most likely candidate in thesystem we describe.

The current state-of-the-art in radiation detector timing resolutionslimits the ability to solely use time-of-flight to determine the lengthalong the outgoing probe photon's trajectory at which the scatteringoccurred. The invention described recovers resolution in this thirddimension by imaging the return scattered photons with adirectionally-sensitive detector positioned on the same side (relativeto the target) as the outgoing probe photon's direction. Even if thedirectionally-sensitive return scatter detector is probabilistic ratherthan deterministic in its sensitivity to return photon direction (in themanner of a coded-aperture imager), the combination of fine directionalsensitivity in the directional detector, and deterministic limiting ofpossible scattering positions in the field-of-view (through outgoingphoton trajectory measurement and time-of-flight information) allows thereconstruction in fine detail while reducing the variance build up theimage formed.

The exemplary embodiments of the invention further reduce variance inthe image using some or all of the following data: time-of-flightinformation, the measured outgoing photon trajectory, thedeterministically measured position of detection of the scatteredphoton, the known energy of the outgoing probe photon, the measuredenergy of the return scattered photon, and the well establishedenergy-versus-scattering-angle relationship in Compton scattering todiscriminate scattered photons that have returned via a single—ratherthan a multiple—scattering interaction. This capability allows furtherimprovement in contrast by only directly placing single-scatteredphotons in the reconstructed image whose scattering position can beestablished through intersection between the outgoing photon's measuredtrajectory and the direction measured of the return scattered photon.

Describing generally an exemplary embodiment of the invention, positronsof sufficiently low energy are captured within a small source-generationregion, where they combine with electrons in atoms in the region andannihilate. A compact positron-emitting radioisotope source either ofsufficient thickness itself to stop some proportion of emittedpositrons, or contained within a source holder of sufficient thicknessto do so, is one method for generating such annihilation events in asmall region. However, the positrons may be generated elsewhere andimpinged on the small source generation region where the recombinationoccurs.

Each annihilation releases a pair of photons, each of approximately 511keV, in coincident pairs that travel in essentially opposite directions.By detecting the direction and time of emission of one photon in thecoincident pair, and through the known location of the smallrecombination region where the annihilation event is known to have takenplace, the trajectory and emission time of the other photon (theoutgoing probe photon) in the coincident pair can be deduced. In thecontext of this document, these outgoing probe photons are referred toas “tagged”.

A target volume to be imaged is exposed to tagged photons. The regionbeing irradiated can be adjusted through collimation to include whateverregion of interest is convenient. The tagged photons traversing thevolume interact with matter in the volume. Many of the interactions willgenerate secondary photons that scatter from atoms in the volume at someangle to the tagged photon's incident trajectory.

A detector system situated at some angle to the outgoing tagged photon'strajectory is sensitive to the direction, time and optionally the energyof any return scattered photons that enter the detection region. Thissub-system will be referred to in this document as the “return-scatterdirectional detector”. Through time-coincidence between the detection ofany scattered photons and the outgoing tagged-photon's deduced time oftraversing the volume being imaged, some fraction of the return photonor photons detected can be associated with the outgoing tagged photonthat generated it.

High-energy photons traversing a material have a non-zero probability oftraveling some finite distance through the material without experiencingany interaction at all. As such, the photon has traveled through thematerial unchanged to this point. Some proportion of the tagged photonsused to irradiate the volume being inspected will penetrate to somedepth within the materials being imaged within the volume, undergo asingle scattering interaction, then exit the volume being imaged withoutundergoing any further interactions. These are referred to in thisdocument as “single-scatter events”. Because photons in this energyrange travel in essentially straight lines between interactions, and wehave directly determined the trajectory of the outgoing tagged photon,we deterministically know that any single-scattered photons detectedhave returned from some point along the outgoing tagged-photon'strajectory. Furthermore, by imaging the return scattered photon's returndirection at some angle to the side of the outgoing tagged-photon'strajectory, the scattering locations of single-scattered photons can bereconstructed in three-dimensions by projecting the imaged scatteredphoton's direction back onto the outgoing tagged photon's trajectory.Techniques for discriminating single- from multiple-scatter events willbe described in the description of the exemplary embodiments thatfollows.

The return-scatter detector may image the return scattered photondirection in one or two dimensions, and in both cases yield sufficientinformation to reconstruct a three-dimensional map of scatteringlocations. Some types of return-scatter detectors may deterministicallylocate the return scatter direction in two dimensions, such as through apinhole-aperture camera, or deterministically in one dimension through aslit-aperture camera. Other types only probabilistically projectpossible return scatter directions. Examples of such imaging devices areCompton cameras or one- or two-dimensional coded aperture arrays. Asignificant point with the present invention is that the outgoingphoton's trajectory is known directly in two dimensions through thephoton-tagging process described above, and that the side imagingthrough the return-scatter directional detector allows projection backto the measured outgoing trajectory to determine the third dimension ofthe scattering location.

The principle photon scattering mechanisms of utility in this invention,and by far the dominant interaction mechanism for photons in the energyrange of 511 keV are Compton scattering and photoelectric absorption.These two mechanisms have different characteristics, both of utility tothis invention.

Compton scattering will produce secondary scattered photons that exit atsome angle from the trajectory of the incident photon being scattered.For Compton scattering from a free and stationary electron, the energyof the scattered photon from a single interaction is completelypredictable from the energy of the incident photon and the angle ofscattering. To a good approximation, the energy and momentum of atomicelectrons in all but the lowest orbitals of the highest-atomic-numberatoms are relatively insignificant in comparison to the energy andmomentum transfers involved in Compton scattering of a 511 keV photon.As such, these energies and momenta can be ignored, and to a goodapproximation the energy of single-scattered photons for most materialsin the volume being imaged can be predicted from the angle ofscattering. Photons whose energy, as measured in the return-scatterdirectional detector, do not match the energy predicted forsingle-scatter events can be rejected from being included in the tallyof single-scatter events. This technique will improve the contrast inthe reconstructed image, by rejecting multiple scatter events whosescattering position cannot be directly determined in three dimensions.

A complicating factor is that some return-scatter directional detectors,for example coded-aperture arrays, do not deterministically measure thereturn angle of every photon detected. Instead, such detectorsprobabilistically assign the scattering location to multiple positionsin the field of view. As such, a one-to-one prediction of thesingle-scatter energies of individual return-scattered photons detectedcannot be made as the assumed single-scatter angle cannot be calculateddeterministically. To overcome this problem, the secondary mechanism ofmeasured time-of-flight between emission of the outgoing tagged photonand detection of the return scattered photon, in conjunction with theknown point of emission of the outgoing tagged photon; itsdeterministically measured outgoing trajectory; and thedeterministically measured point of detection of the return scatteredphotons; is employed through simple trigonometry to estimate the angleof an assumed single-scatter event. From this, an estimate of theexpected single-scatter-return-photon energy can be made and asingle-scatter energy window applied to return-scattered photons topreferentially select single-scattered photons over multiple-scatteredphotons. In more general terms, all measured information available, suchas outgoing tagged-photon trajectory,time-of-flight-single-scatter-energy prediction, measured return-photonenergy and any probabilistic return-angle information from thereturn-scatter angular detector are combined to optimally projectprobability of scattering location out to the three-dimensional field ofview in the volume being inspected.

In low to moderate atomic number materials, in the energy range of theoutgoing tagged photon and single-scatter return photon energies,Compton scattering is by far the dominant photon interaction mechanism.The photon attenuation mechanism in Compton scattering producessecondary scattered photons that can be detected. As such, we canestimate the attenuation of photons traversing through material within avolume, by measuring the number of secondary photons scattering sidewaysout of the volume. Once an optimal estimate of return scatteringlocations has been reconstructed within the three-dimensional volumebeing inspected, a secondary iterative process can be invoked in whichthe estimates of the radiographic density along the path through whichprimary tagged photons have entered into and traversed through thevolume being imaged, and along the paths through which scattered photonshave returned from the volume to the return-scatter directionaldetector, is used to compensate for attenuation along both paths. Theradiographic density of materials in the foreground is directlyestimated from the flux of single-scattered photons detected from thesematerials. These estimates are then used to progressively estimate theattenuation of the tagged-photon illumination and the return-scatteryields from materials behind the foreground materials. From this, athree-dimensional maximum-likelihood estimate of the three-dimensionalradiographic density throughout the volume being imaged can beestablished, at least to a depth where sufficient photon statistics areavailable, and cumulative errors in the radiographic density have notcaused divergence of the density estimates.

In higher-atomic-number elements in materials within the volume, theproportion of photo-electric absorption events to Compton scatteringwill be higher. In a photoelectric absorption event, all of the incidentphoton energy is transferred to an atomic electron within the volume,and no secondary scattered photon is produced (at least in many casesnot of an energy adequate to exit the volume and make it to thereturn-scatter detector). This may frustrate some of the attempts toiteratively estimate radiographic density at depth within the volume.However, it is also possible that sufficient information will beavailable to discriminate higher-atomic-number materials throughout thevolume by detecting components sections within the volume in which theattenuation of both the incident tagged photons and exiting scatteredphotons is higher in proportion to the amount of scatter being measuredfrom such component sections. This would rely on gauging scatter fromobjects behind the object in question. Imaging from several differenttagged-photon source and return-scatter detector positions could helpwith separating out such effects, as could knowledge of some of theelemental composition of materials in the field of view, such as assumedmaterials in body paneling of automobiles being imaged.

As mentioned previously, the photoelectric absorption mechanism knocksan electron from an atom. The ionized atom is then left with a vacancyin one of its atomic-state orbitals. The subsequent re-capture of anelectron, or de-excitation of the ionized atom will often lead to theemission of either an optical or an x-ray photon. In the case of thehighest-atomic-number materials the de-excitations from ionizations ofdeep core atomic electrons can produce x-ray photons in the order of 100keV. In such cases, in certain configurations of materials within thevolume, it may be possible to directly detect these x-rays, and to imageand directly identify the location and elemental composition of suchhigh-atomic-number elements within the volume.

Turning to the drawings, in which like numerals indicate like elementsthroughout the figures, exemplary embodiments of the invention aredescribed in detail. Referring now to FIG. 1, an exemplary embodiment ofa system 100 using annihilation coincidence photons forthree-dimensional imaging is illustrated. As shown in FIG. 1, theimaging system 100 can be placed in a vehicle 105 for mobility. Theimaging system 100 comprises a positron source 110, a photon tagger 112,and a return-scatter directional detector 130. In the exemplaryembodiment 100, the positron source 110 comprises a radioisotope thatemits positrons, such as a pellet of radioactive Na-22. The emittedpositrons combine with electrons either within the positron source 110or within a holder surrounding the positron source. When a positron andelectron combine, they annihilate each other forming two photons thattravel in essentially opposite directions. In the preferred embodimentof system 100, a holder surrounding the positron source 110 comprisestwo diametrically placed windows which are opened to release the twophotons.

The photon tagger 112 positioned outside one of the windows of theholder detects the direction and time of emission for one photon in thecoincident pair. For example, the photon tagger 112 can be a high-speedposition-sensitive gamma photon detector widely used in nuclearmedicine. The photon tagger 112 can measure in two dimensions thephoton's point of intersection with the surface of the photon tagger112. Using the recombination location where the annihilation took placeand the detected direction and time of emission measured by the photontagger 112, a computing device coupled to the photon tagger 112 cancalculate the trajectory and emission time of the outgoing probe photon.

A collimator can be used to direct a beam of outgoing probe photons 115towards a target volume 120 that is to be imaged. The outgoing probephotons 115 are able to penetrate the target volume 120, however, thedose of photons is small enough that it does not present health hazardsfor nearby people. A certain volume of backscatter photons 125 aredirected from the target volume 120 to the return-scatter directionaldetector 130. As described above, a variety of different detectors canbe used as the return-scatter direction detector 130. Detecting thebackscatter photons 125 allows the exemplary system 100 to create animage of the volume elements (“voxels”) within the target 120. In thepreferred embodiment, the system 100 can create a three-dimensionalimage of the target 120 with a resolution of 1.5 cm.

Target objects with densities comparable to or less than water can beimaged to a depth of several centimeters. Target objects with higherdensities do not permit significant penetration of the outgoing probephotons 115. Focal length adjustments to the outgoing probe photons 115and the return-scatter direction detector 130 in conjunction withincreased acquisition time can yield enhanced imaging resolution for thepenetrable region of higher density objects.

The imaging method with exemplary system 100 relies on photons thatreturn through only one scatter, as opposed to multiple scatteringinteractions. Each photon in the backscatter photons 125 is measuredwith respect to its energy, the time each reaches detector 130, and theposition at which it strikes the detector 130. Using this informationmeasured at the return-scatter direction detector 130, coupled with theinformation measure by the photon tagger 112 and the well-known Comptonenergy-versus-scattering-angle relationship, allows the exemplary system100 to identify and discard photons from multiple-scatter or backgroundevents. By limiting the data to single-scatter events, the system 100can improve image quality and contrast as compared to the broad energyspread in photons used in x-ray based backscatter imagers.

Referring to FIG. 2, a top-view schematic illustration is provided foran exemplary embodiment of the present invention. Exemplary imagingsystem 150 illustrated in FIG. 2 comprises tagged photon source 160 andbackscatter directional detector 155. As described previously, thedirection and time of the outgoing probe photon 165 are determined atthe tagged photon source 160. The outgoing probe photon 165 collideswith target volume 170 and backscattered photon 175 is detected by thebackscatter directional detector 155.

An imaging software module installed on a computing device receives thedata collected at the tagged photon source 160 and the data collected atthe backscatter directional detector 155 and reconstructs aone-dimensional image along the known tagged track of the outgoing probephoton 165. If the imaging software module determines, based on thecollected energy and time data, that the backscattered photon 175 wasscattered more than once, the data for that photon is discarded from usein constructing the image of the target. Data for single-scatter photonsis collected over a period of time, such as three minutes, and theimaging software module can build a three-dimensional image of thetarget.

Referring to FIG. 3, an exemplary method for tagging an outgoing probephoton is illustrated. FIG. 3 shows a photon tagger 305, a radioisotopesource 310, a first photon 315 and an outgoing probe photon 320. Asshown in FIG. 3, the position of the radioisotope source 310 and,therefore, the point at which the photons are generated from apositron-electron collision are both known. The photon tagger 305, suchas those used in PET medical imaging, intercepts the first photon 315and measures both the trajectory and emission time of the interceptedfirst photon 315. The data the photon tagger 305 collects from theintercepted first photon 315 permits an imaging software moduleinstalled on a computer to determine the trajectory of the outgoingprobe photon 320.

An exemplary photon tagger, such as photon tagger 305, typicallycomprises a segmented scintillator optically coupled to a number ofphotomultiplier tubes (PMT) or avalanche photodiodes (APD). Thescintillator converts each photon received into a pulse of opticalphotons. Because of the high count rates involved, a fast scintillator,such as lutetium oxyorthosilicate (LSO) is preferred. The PMTs or APDsdetect the optical photons and generate an amplified electrical pulse.

A standard technique for a photon tagger is to place multiple PMTs onthe back of the scintillator. The light pulses are generated at thepoint of initial scattering of the first photon in the scintillator andat possible subsequent secondary scattering sites close to this initialinteraction point. By measuring the relative amount of light sharedbetween the PMTs, the point the photon entered the detector can beestablished.

With respect to the positron source, a radioisotope with an activity ofapproximately 20 millicurie should be sufficient for the imaging. Oneexample of a commercially available holder that can be used forcontaining the source is an Ohmart-Vega rotary shutter source holdersuch as the SHLD-1.

Referring to FIG. 4, a one-dimensional coded aperture mask pattern anddetector array in accordance with an exemplary embodiment of theinvention is illustrated. The coded aperture detector 405 comprises apatterned mask 410 positioned in front of a detector array 415. Thepatterned mask 410 is typically 50% open with the mask being thickenough to stop the backscatter photons except for those backscatterphotons that pass through the openings in the patterned mask 410.

Arrow 420 in exemplary FIG. 4 points to a single hit of a backscatterphoton on a single detector in detector array 415. Arrows 430 illustratesome of the many other possible directions from which the photon couldhave arrived at the detector. Absent other information, it would bedifficult to determine from which direction a single photon arrived.However, after a certain number of photons are detected by detector 405,the points in the field of view consistent with the arrivals quicklynarrows down to a single point.

A reconstruction kernel, such as the example illustrated in FIG. 5, cantrack the detected photons arriving at the various detectors in thedetector array 415. The reconstruction kernels project back to theoutside world a probability map of positions from which each photoncould have arrived. Each detector in the detector array 415 typicallyhas a different reconstruction kernel. The reconstruction kernel shouldincorporate all known a-priori information about the relativeprobabilities of arrival from all the possible source locations for eachdetected photon.

The exemplary imaging system, such as those described in connection withFIGS. 1 and 2, has significant a-priori information about the photonsintercepted at the coded aperture detector 405. Because the trajectoryof the outgoing probe photon is known from the measurements at thephoton tagger, the only possible return scattering locations are on themeasured line of the outgoing probe photon's track. Additionally,because the imaging system measures the outgoing time and return time ofeach photon, the track of the outgoing probe photon can be limited to acertain range based on the measured time data.

The reconstruction kernel illustrated in FIG. 5 is a calculated optimalreconstruction kernel for a photon hit at the coded aperture detector.The reconstruction kernel shown in FIG. 5 was derived to locate a sourceat an assumed distance of 75 meters from an imaging system. The positivesections of the kernel add probability to the photon track sectionsvisible through the mask, whereas the negative sections subtractprobability for the photon track sections blocked by the mask.

A desirable characteristic in a coded aperture mask is the so-called“ideal response.” For each hit on a detector, a probability can bedispatched to the field of view that the photon arrived through any ofthe open sections. Each hit at the detector dispatches probability tomany places from which the photon did not arrive. While this isunavoidable, a mask pattern can be selected that, on average, dispatchesthe maximum probability to the correct point and a flat uniformprobability to other points in range of the kernel. In fact, codedaperture masks with an autocorrelation function that is a single centralpeak with flat trails exhibit this ideal response.

FIG. 6 illustrates a calculated point-spread-response for an imager witha focal length of 210 cm from mask to detector. The full-width at halfmaximum corresponds to 40-milliradian resolution at 75 meters. For thepurposes of a backscatter directional detector optimized for applicationin this invention, the coded-aperture pitch (finest feature size), rank(number of pitch element widths before the coded-aperture patternrepeats), and focal length (coded-aperture to detector spacing) would beoptimized based on factors such as the finest feature size resolvable bythe detector behind the coded aperture, the system time-of-flight timingresolution, and the average distance to the target. A resolving power onthe order of 1.5 cm at the target is anticipated when optimized for adistance of three meters to target.

Multiple counts on multiple detectors are dispatched through thereconstruction kernel to build an image with a sharpness given by thesystem's point spread function. However, the kernel adds variance over awider range. The process can be understood by imagining photons randomlyentering from a single point source in the field of view. The photonswill come through various open sections of the mask and hit variousdetectors; each hit will dispatch probability out to the field of view.The correct point in the field of view will always be receiving positivecontributions from the various reconstruction kernels from the variousdetectors hit. Incorrect points nearby will sometimes receive positivecontributions and sometimes receive negative contributions. The mean ofthese contributions for incorrect points will tend to zero; however, thevariance from these contributions adds up over the entire non-zero widthof the kernels. Fortunately, in our application, a-prioritagged-photon-track and range-gating information limit these kernelwidths to a small volume. This noise variance only spreads out along thedirection imaged by the coded aperture. The photon tagger for eachphoton measures the other two directions deterministically, so there isno variance spread in these other two directions.

To demonstrate the expected noise variance spread in an exemplaryimaging system, one can imagine a single column of voxels in thereconstruction volume aligned along the direction of the tagged photonflow. Approximately 324 single-scatter photons are available forradiographic imaging of each column of voxels, assuming a 20 millicuriesource, a three-minute imaging time, a 2-meter standoff, and 1.5 cm cubevoxels. FIG. 7 illustrates an example where 81 counts (left side) and243 counts (right side) (totaling 324) have been reconstructed into acolumn of forty 1.5 cm voxels. Eighty-one counts represents the 25%single-scatter probability of 324 photons from 1 mm of body panel andthe 243 counts represent the residual (from 324) remaining to scatterwhen encountering a radiographically-thick object. The reconstructionnoise will spread over 40 channels because they represent the non-zerolength of reconstruction kernel that a 2-nanosecond-range-gatingprecision implies.

The two plots shown in FIG. 7 simulate the reconstructed radiographicprofile and expected noise for a single line of voxels that have imagedthrough a thin and a thick surface respectively in the target vehicle.We have plotted noise with a standard deviation equal to the square rootof the counts on each channel and a central peak equal to the counts.Even with only 81 counts, the signal appears clearly above the noise.

Single-scatter coincident return photons can be assigned to the voxelsaround the inferred scattering location. However, for each returnphoton, the outgoing photon had to make it from the radioisotope sourceto the scattering site and the return photon back from the scatteringsite to the coded aperture detector. A maximum-likelihood reconstructioncan be used to solve for a consistent radiographic density from thescattered photon data. The first image reconstruction step will simplybe to populate a voxelized volume with the projected 3D locations ofsingle scatter events. This essentially treats the photons from thesource as a “spray paint” that has fallen through the imaging region andprogressively deposited on the regions of radiographic densityencountered. A second stage of reconstruction then takes thisinformation and projects back to estimate both the flux irradiating thisvoxel from the source, and the probability that a scattered ray fromthis location makes it through the rest of the reconstruction region tothe detector. This iterative approach will attempt to assignradiographic density correctly throughout the inspection volume, atleast in regions with reasonable return scatter intensity.

Gamma and x-ray photons interact with matter almost exclusively by themechanisms of photoelectric absorption, Compton scattering, and pairproduction. At the energy levels found with photons used in theexemplary imaging systems described in FIGS. 1 and 2, Compton scatteringaccounts for approximately 99% of the photon interactions. In Comptonscattering, an incident photon interacts with an electron. Some energyand momentum of the incident photon transfer to the electron with thebalance carried off in a scattered photon, as illustrated in FIG. 8. Theincident photon's energy and angle of scatter determine the scatteredphoton's energy. The scattered photon's energy is given byE=1/1+α(1−cos(φ))where the scattered photon's energy and the incident photon's energy areexpressed in fractions of the rest mass energy of an electron m_(e)c².The photon's scattering angle from its incident direction is φ. In thecase of the exemplary embodiments described herein, the incident photonenergy is α=1, or 511 keV. Photons of this energy that scatter by 90degrees end up with exactly half this energy. The probability ofscattering as a function of scattering angle is a well-defined functiondepending only on angle and energy.

Radiographic density for Compton scattering is determined by the densityof electrons in the target material and the incident photon energy. Thepresent exemplary embodiments of the invention can achieve goodthree-dimensional image resolution, while also given a 3-dimensional mapof radiographic density to a depth of two or three voxels into a targetwith a density comparable to ammonium nitrate fuel oil (ANFO)explosives, namely 0.84 grams/cm³.

The imaging software module can use timing and energy data collectedwith respect to the outgoing probe photon and the backscattered returnphoton to identify single scatter photons for imaging reconstruction.Single scatter photons provide an image with improved contrast andreduced noise. The timing information collected for both the outgoingprobe photons and the backscatter return photons allows the imagingsoftware module to range-gate the total photon track length to aresolution of about 60 cm. From the known trajectory of the outgoingprobe photon, the round trip time of flight of the detectedbackscattered return photon, and the position of the detector in thecoded aperture imager registering a hit, the imaging software module candirectly calculate the angle from which the photon has returned.

When a detector in the detector array registers a backscattered returnphoton, the distance between the source and the detector in the detectorarray can be calculated and is known as the baseline. The fixed knownbaseline is illustrated in FIG. 9. For example, assume a right-anglescatter where the source-to-scatter distance and the scatter-to-detectordistance are both 3 meters as shown in FIG. 9. The source-to-detectorbaseline in this case is 3√2 meters. The return photon will havescattered by an angle of exactly 90 degrees and have exactly 50% of theoutgoing 511 keV in energy (as shown by the Compton scattered photonenergy formula in the previous section). Alternatively, as alsoillustrated in FIG. 9, if there is a two-nanosecond error in the time offlight measurement and the photon actually traveled a round-tripdistance of 60 cm more, the angle of return of the backscattered photonis more acute—100.4 degrees—and the return energy of the scatteredphoton would be 8% lower—45.9% of 511 keV.

In view of these calculations illustrated in FIG. 9, the energy ofsingle-scatter return photons can be predicted to an accuracy ofapproximately 8%. Photons outside of this energy range can be assumed toresult from multiple scatterings or an accidental coincidence with abackground event and therefore be rejected for purposes of the imaging.To determine what proportion of multiple scatter events should berejected, FIG. 10 illustrates a simple calculation of the energy of a511 keV photon after two sequential scatterings whose sum is 90 degrees.The horizontal axis is the first scattering angle. The vertical axis isthe final photon energy, relative to that of a single 90-degree scatter(namely 256 keV). Superimposed on the illustration in FIG. 10 is anassumed 18% energy resolution on our return photon detection system.This is allocating 8% of uncertainty to the expected return photonenergy and a 10% energy-resolution limit in the backscatter directionaldetector. Scatter events with an energy outside the two horizontal bandsshown in FIG. 10 can be rejected as multiple scatter events. Asillustrated in FIG. 10, if the first or the second scatter angle iszero, the resultant energy is that of a single scatter. Two consecutive45-degree scatterings yield a maximum energy, while a first scatter of90 degrees followed by a backscatter of 180 degrees yields a minimum.The plot shown in FIG. 10 is merely a first approximation because itonly considers scattering in the plane and does not consider thecross-sections of the various scattering angles.

Referencing the reconstruction kernel discussed previously, an optimalkernel will use all of the available information to maximize thesignal-to-noise ratio in the reconstruction. We have just discussedrange gating and energy resolution to discriminate single-scatter frommultiple scatter events. When addressing the reconstruction kernelpreviously, we applied range gating to limit the length of the outgoingphoton track over which the coded aperture reconstruction kernel isapplied, but did not incorporate energy information. Applying energyinformation, if the energy of the backscattered return photon issomewhat higher than the center energy that the range gating wouldimply, the coded aperture reconstruction kernel can be biased toward thelower scattering angle end to reconstruct this event. Similarly, lowerenergy events should bias the kernel to the higher end of its range. Inthis manner, the reconstruction uses all available information toreconstruct the image optimally.

The density of the target will determine the depth to which the probephotons can create an image of the target. Taking ANFO as a referencedensity, the probability that a photon travels some distance withoutinteracting is P_(E)(l)=exp(−1/λ_(E)), where λ_(E) is the expectedlength of travel for a photon of energy, E. This coefficient depends onenergy and the electron density in the scattering material. For ANFO at511 keV, λ_(E) is 13.1 cm; a 90-degree scattered photon has an energy of256 keV and λ_(E) of 10.1 cm.

A single scatter photon must travel into the material of the target andback out without subsequent scattering. The probability that a photonmakes it through a length l of material at 511 keV and then that lengthl again of material at 256 keV, the probability can be estimated by theproduct of the two probabilities:P _(E1)(l)×P _(E2)(l)=exp(−l/λ _(E1))×exp(−l/λ_(E2))=exp(−1(1/λ_(E1)+1/λ_(E2))).

The mean scattering lengths combine into a combined parameter,1/λ_(tot)=(1/λ_(E1)+1/λ_(E2)). The joint average length parameter is1/(1/10.1+1/13.1) cm=5.7 cm. Assuming 45-degree entry and exit anglesimplies that we sample to a depth of 1/√2 of 5.7 cm, which is 4.0 cm.

The foregoing calculation calculates the probability of traversal forentry and exit, assuming the exit angle is also 45 degrees. Additionalsimulations refine this and indicate that the average depth ofsingle-scatter photons returning from a 45-degree angle of incidence isa depth of 3.4 cm in ANFO. Assuming a resolution of 1.5 cm, the imagedepth will include at least two voxels in a material with a density ofANFO and, consequently, will allow estimation of the radiographic volumedensity of the material.

To estimate expected count rates and backscatter return photon yields,we need estimates of the fraction of photons entering a thick targetthat exit via a single scatter. Simulations for 511 keV photonsimpacting a solid rectangular block of ANFO for various incidence anglesare shown in the following table:

Single-Scatters Single-Scatter Degrees in 100,000 Percent 0 49,979 50.0%15 22,080 22.1% 30 13,725 13.7% 45 10,268 10.3% 60 8,417  8.4% 75 7,775 7.8% 90 7,496  7.5%

A positron annihilation source of 20 millicurie, with 3.7×10¹⁰disintegrations per curie and two photons per disintegration, yields aphoton flux at 1 meter of 1.17×10⁵ photons per cm² per second. We assumethat the backscatter directional imaging detector (e.g., a codedaperture detector) has an area of 0.925 m² and is behind a codedaperture mask with a 50% open factor. If we assume the worst-casesingle-scatter-exit probability for a normal incidence of 7.5% anddistribute this return flux uniformly over a 3-meter radius half sphere,we estimate that each square centimeter of target irradiated returns 144single-scattered photons.

Each column of 1.5 cm voxels aligned toward the source is illuminated by144×(1.5)²=324 photons. This is not large and would be inadequate for ageneral 3D volumetric reconstruction. However, much of the target isempty space. If 324 single-scatter return photons are available, fallingthrough each voxel column and scattering on encountering materialdensity, on average, once we've traversed to a depth of 3.4 cm AMFOdensity (assuming 45-degree entry and exit paths), we will have depletedthe available single-scatter photons to a level of 1/e of the originalflux. Those single-scatters we do detect are dispatched directly (onaverage) to the actual 3D location of their scattering. FIG. 7 offers anindication of how accurately we could reconstruct density in traversinga single line of voxels in which we had a return of 81 and 243 photons.

Background photons from other sources can affect the data collected atthe backscatter imaging detector. However, the effect of these otherbackground photons can be minimized by shielding the back and sides ofthe backscatter imaging detector. Measuring the timing and energy of thebackscatter return photons also allows for identifying and filtering outbackground photons from the relevant data collected at the backscatterimaging detector.

Referring now to FIG. 11, an exemplary method 1100 for performingimaging using annihilation coincidence photons is illustrated inaccordance with one embodiment of the invention. Those of skill in theart will recognize that exemplary method 1100 is only one way toaccomplish the invention and that alternate embodiments of the inventioncan involve adding steps to or removing steps from method 1100.

Exemplary method 1100 begins with step 1102 where the imaging system isplaced along side a target. In the preferred embodiment, the imagingsystem is mounted in a vehicle that can drive up along side a variety oftargets which can include other vehicles and other stationary objects.As described in step 1104, a decaying radioisotope source emitspositrons. Although not required, typically, the decaying radioisotopesource is placed inside a source holder that is part of the entireimaging system. The emitted positron collides with an electronannihilating the two particles and emitting two coincident photonstraveling in opposite directions as referenced in step 1106. In thepreferred embodiment, the annihilation occurs within the source holder.

In step 1108, one of the emitted photons is detected by a nearby photontagger (also referred to as a gamma detector). The photon tagger is acommercially available piece of equipment that is able to determine thetrajectory and an emission time for the detected photon. In step 1110,an imaging software module designed for processing the collected datacalculates the trajectory and emission time for the other photontraveling in the opposite direction towards the target. The other photontraveling in the opposite direction away from the photon tagger collideswith the target and generates a backscatter photon in step 1112. Whilethere may be multiple collisions within the target, the preferredembodiment is primarily interested in photons that undergo only onescattering event with the target before being detected by an imagingdetector.

In step 1114, the imaging detector detects the trajectory and timingassociated with a backscattered photon when it collides with the imagingdetector. A variety of imaging detectors can be used, but, as describedabove, the preferred embodiment implements a coded aperture imager. Theimaging detector is typically part of the complete imaging system andcan be positioned, for example, toward the rear of a vehicle asillustrated in FIG. 1. In step 1116, the imaging software module usesthe data collected from the imaging detector and the data collected fromthe photon tagger for multiple photons and reconstructs the targetimage. The imaging software module can process a variety of collecteddata to reconstruct the target image. For example, in addition to themeasured trajectories and measured times for the outgoing probe photonand the returning backscattered photon, the imaging software module canalso use the measured energy level for the returning backscatter photonand the known energy of the outgoing probe photon.

The invention comprises computer programs, such as the exemplary imagingsoftware module described above, that embody the functions describedherein and that are illustrated in the appended flow charts. However, itshould be apparent that there could be many different ways ofimplementing the imaging software module in computer programming, andthe invention should not be construed as limited to any one set ofcomputer program instructions. Further, a skilled programmer would beable to write such a computer program to implement an exemplaryembodiment based on the flow charts and associated description in theapplication text. Therefore, disclosure of a particular set of programcode instructions is not considered necessary for an adequateunderstanding of how to make and use the invention. The inventivefunctionality of the claimed computer program will be explained in moredetail in the following description read in conjunction with the figuresillustrating the program flow.

FIG. 12 illustrates a conventional computing device 220 suitable forsupporting the operation of the imaging software module in the preferredembodiment of the present invention. The conventional computing device220 can receive data from the photon tagger and the backscatter returnphoton detector via any one of a variety of conventional datacommunication links. In FIG. 12, the computing device 220 operates in anetworked environment with logical connections to one or more remotecomputers 211. The logical connections between computing device 220 andremote computer 211 are represented by a local area network 273 and awide area network 252. Those of ordinary skill in the art will recognizethat in this client/server configuration, the remote computer 211 mayfunction as a file server or computer server. Those of ordinary skill inthe art also will recognize that the invention can function in astand-alone computing environment.

The computing device 220 includes a processing unit 221, such as“PENTIUM” microprocessors manufactured by Intel Corporation of SantaClara, Calif. The computing device 220 also includes system memory 222,including read only memory (ROM) 224 and random access memory (RAM) 225,which is connected to the processor 221 by a system bus 223. Thepreferred computing device 220 utilizes a BIOS 226, which is stored inROM 224. Those skilled in the art will recognize that the BIOS 226 is aset of basic routines that helps to transfer information betweenelements within the computing device 220. Those skilled in the art willalso appreciate that the present invention may be implemented oncomputers having other architectures, such as computers that do not usea BIOS, and those that utilize other microprocessors.

Within the computing device 220, a local hard disk drive 227 isconnected to the system bus 223 via a hard disk drive interface 232. ACD-ROM or DVD drive 230, which is used to read a CD-ROM or DVD disk 231,is connected to the system bus 223 via a CD-ROM or DVD interface 234. Inother embodiments, other types of storage devices such as external harddisk drives and USB thumb drives can be used. A user enters commands andinformation into the computing device 220 by using input devices, suchas a keyboard 240 and/or pointing device, such as a mouse 242, which areconnected to the system bus 223 via a serial port interface 246. Othertypes of pointing devices (not shown in FIG. 12) include track pads,track balls, pens, head trackers, data gloves and other devices suitablefor positioning a cursor on a computer monitor 247. The monitor 247 orother kind of display device is connected to the system bus 223 via avideo adapter 248.

The remote computer 211 in this networked environment is connected to aremote memory storage device 250. This remote memory storage device 250is typically a large capacity device such as a hard disk drive, CD-ROMor DVD drive, magneto-optical drive or the like. Those skilled in theart will understand that software modules are provided to the remotecomputer 211 via computer-readable media. The computing device 220 isconnected to the remote computer by a network interface 153, which isused to communicate over the local area network 173.

In an alternative embodiment, the computing device 220 is also connectedto the remote computer 211 by a modem 254, which is used to communicateover the wide area network 252, such as the Internet. The modem 254 isconnected to the system bus 223 via the serial port interface 246. Themodem 254 also can be connected to the public switched telephone network(PSTN) or community antenna television (CATV) network. Althoughillustrated in FIG. 12 as external to the computing device 220, those ofordinary skill in the art can recognize that the modem 254 may also beinternal to the computing device 220, thus communicating directly viathe system bus 223. Connection to the remote computer 211 via both thelocal area network 273 and the wide area network 252 is not required,but merely illustrates alternative methods of providing a communicationpath between the computing device 220 and the remote computer 211.

Although other internal components of the computing device 220 are notshown, those of ordinary skill in the art will appreciate that suchcomponents and the interconnection between them are well known.Accordingly, additional details concerning the internal construction ofthe computing device 220 need not be disclosed in connection with thepresent invention.

Those skilled in the art will understand that program modules, such asan operating system 235 and other software modules 260 a, 263 a and 266a, and data are provided to the computing device 220 viacomputer-readable media. In the preferred computing device, thecomputer-readable media include local or remote memory storage devices,which may include the local hard disk drive 227, CD-ROM or DVD 231, RAM225, ROM 224, and the remote memory storage device 250.

In conclusion, the invention, as represented in the foregoing exemplaryembodiments, provides systems and methods for imaging a target objectusing coincident photons created during an electron-positronannihilation. As described in the foregoing exemplary embodiments, thetrajectory and timing of the photons can be used track the photons asthey collide with a target and create backscattered photons that aredetected and used to create an image of the target.

The embodiments set forth herein are intended to be exemplary. From thedescription of the exemplary embodiments, equivalents of the elementsshown herein and ways of constructing other embodiments of the inventionwill be apparent to practitioners of the art. For example, while thecomponents of the imaging system are located together in a vehicle inthe preferred embodiment, in other embodiments the components can beseparated or located at different positions around the target.Similarly, in other embodiments the imaging software module can performdifferent types of analyses to either consider or filter return photonsthat undergo multiple scattering collisions. Many other modifications,features and embodiments of the invention will become evident to thoseof skill in the art. It should be appreciated, therefore, that manyaspects of the invention were described above by way of example only andare not intended as required or essential elements of the inventionunless explicitly stated otherwise. Accordingly, it should be understoodthat the foregoing relates only to certain embodiments of the inventionand that numerous changes can be made therein without departing from thespirit and scope of the invention.

1. A method for creating an image of a target, the method comprising:arranging a radioisotope source that emits positrons that collide withelectrons, the collision emitting a first photon and a second photon;measuring by a gamma detector a first trajectory and a first timeassociated with the first photon; calculating by an imaging softwaremodule installed on a computer a second time and a second trajectoryassociated with the second photon; detecting by an imaging detector ascattered photon created from a collision between the second photon anda target, the imaging detector measuring a scattered trajectory and ascattered time associated with the scattered photon; and calculating bythe imaging software module a position of the target based on the secondtime, the second trajectory, the scattered time and the scatteredtrajectory.
 2. The method of claim 1, wherein the imaging detector is acoded aperture imager comprising an array of detectors and a patternedmask.
 3. The method of claim 1, wherein the radioisotope source and theimaging detector are located on one side of the target such that theangle between the second trajectory of the second photon and thescattered trajectory of the scattered photon is less than 180 degrees.4. The method of claim 1, further comprising the step of the imagingsoftware module filtering a second scattered photon based on a secondscattered time associated with the second scattered photon.
 5. Themethod of claim 1, further comprising the step of the imaging softwaremodule filtering a second scattered photon based on a second energylevel associated with the second scattered photon.
 6. The method ofclaim 1, further comprising the step of opening a first window and asecond window in a source holder in order to emit the first photon andthe second photon.
 7. The method of claim 1, further comprising the stepof the imaging software module estimating the density of the targetbased on data collected by the gamma detector and the imaging detector.8. A system for creating an image of a target, the system comprising: aradioisotope source that generates a positron that collides with anelectron and emits a first photon and a second photon; a photon taggermeasuring a first trajectory and a first time associated with the firstphoton; an imaging software module installed on a computer, the imagingsoftware module receiving the first time and the first trajectoryassociated with the first photon and calculating a second trajectory anda second time associated with the second photon; a target that interactswith the second photon and emits a scattered photon; a detectormeasuring a scattered trajectory and a scattered time associated withthe scattered photon, wherein the imaging software module calculates aposition of the target using the scattered trajectory and the scatteredtime associated with the scattered photon and the second trajectory andthe second time associated with the second photon.
 9. The system ofclaim 8, wherein the detector comprises shielding to reduce the numberof background photons that reach the detector.
 10. The system of claim8, wherein the detector is a coded aperture imager comprising an arrayof detectors and a patterned mask.
 11. The system of claim 8, whereinthe radioisotope source and the detector are located on one side of thetarget such that the angle between the second trajectory of the secondphoton and the scattered trajectory of the scattered photon is less than180 degrees.
 12. The system of claim 8, wherein the imaging softwaremodule filters a second scattered photon based on a second scatteredtime associated with the second scattered photon.
 13. The system ofclaim 8, wherein the imaging software module filters a second scatteredphoton based on a second energy level associated with the secondscattered photon.
 14. The system of claim 8, further comprising a sourceholder for containing the radioisotope source, wherein the source holdercomprises a first window for emitting the first photon and a secondswindow for emitting the second photon.
 15. The system of claim 8,wherein the imaging software module estimates the density of the targetbased on the data collected from the photon tagger and the detector. 16.A computer program product comprising an imaging software module storedon a non-transitory computer-readable medium, the imaging softwaremodule comprising: instructions for receiving a first trajectory and afirst time from a gamma detector, the first trajectory and the firsttime associated with a first photon, the first photon being part of aphoton pair generated from a collision between a positron and anelectron; instructions for calculating a second time and a secondtrajectory associated with a second photon, the second photon being partof the photon pair; instructions for receiving a scattered trajectoryand a scattered time from an imaging detector, the scattered trajectoryand the scattered time associated with a scattered photon generated froma collision between the second photon and a target; instructions forcalculating a position within the target based on the second time, thesecond trajectory, the scattered time and the scattered trajectory. 17.The computer program product of claim 16, further comprising:instructions for receiving a second scattered trajectory and a secondscattered time from the imaging detector, the second scatteredtrajectory and the second scattered time associated with a secondscattered photon; and instructions for filtering the second scatteredphoton based on the second scattered time.
 18. The computer programproduct of claim 16, further comprising: instructions for receiving asecond scattered trajectory and a second scattered energy level from theimaging detector, the second scattered trajectory and the secondscattered energy level associated with a second scattered photon; andinstructions for filtering the second scattered photon based on thesecond scattered energy level.
 19. The computer program product of claim16, wherein the positron is emitted by a radioisotope source.
 20. Thecomputer program product of claim 16, further comprising: instructionsfor estimating the density of the target based on the data collectedfrom the scattered detector and the imaging detector.